Skip to content# Changing the Subject of a Formula: Comprehensive Guide with Worksheet

## What is changing the subject of a formula?

## How to change the subject of a formula

## Exam Tips

**Solution:**

## Conclusion

## Worksheet on Changing the Subject of a Formula

**Changing the Subject of a Formula**

- Changing the subject of a formula is one of the essential skills in algebra, which removes the expressions of a specific variable in favour of others.
- Whether you’re handling physics equations or financial formulas, having the ability to change the definition of a subject lets you adjust equations to your needs.

In this article, we will discuss:

**What is changing the subject of a formula?****How to change the subject of a formula?**

Here is one more link to practice a few extra questions: Maths Genie Changing the Subject of a Formula Questions

**Definition:**

- Rearranging an equation is known as changing the subject, which is the process of highlighting the variable of choice as the most important factor in the equation.
- This manipulation facilitates in separate and clearer understanding of the behaviour of specific variables in a particular mathematical concept.

**Importance:**

- First, these skills aids in problem solving, giving us the chance to examine the outcomes of individual variables.
- Shows directly how the relationships between the mathematics are established.

**Identify the Target Variable:**- Determine which variable needs to be isolated as the new subject of the formula.

**Inverse Operations:**- Utilize inverse operations to manipulate the equation and isolate the desired variable.
- Common inverse operations include addition and subtraction, multiplication and division.

**Maintain Equality:**

- Perform the same operations on both sides of the equation to keep it balanced.

** **

** **

**Solved Example: **

**Question 1: In regards to the quadratic equation ax ^{2} + bx + c = 0 with a, b, and c being constants. Replace the subject of the formula by x to isolate the variable x.**

Solution:

**Step #1: Indicate the Target Variable**

In this case, we aim to isolate the variable x and make it the subject of the quadratic equation.

**Step #2: Use the Quadratic Formula**

The quadratic formula is a useful mean for us to extract x of a quadratic equation of type ax^{2} + bx + c = 0.

Using this formula, a, b and c are the coefficients of the quadratic equation.

**Question 2: Given E = mc ^{2}, change the subject to m.**

Solution:

**Step#1:**Indicate the Target Variable:**m****Step #2:**Divide both sides by**c**:^{2}

** m = E/c ^{2}**

**Importance of Formula Manipulation:**

- Enhances problem-solving capabilities.
- Provides us with the ability to understand maths in a more refined manner.

**Common Techniques in Changing the Subject:**

- Identifying the target variable.
- Adjusting the value of the variable opposite while keeping an equation balanced.

**Applications Across Disciplines:**

- Physics: The variables separate from the equation of motion or energy, for instance.
- Finance: Analyzing formulas for compound interest or investment returns.

**Practice Questions**

Question 1: How can you change the subject of the formula A = ½ bh to find h(height)?

Answer :**Step #1:** Isolate h

**A = ½ bh**

Multiply both sides by 2/b to get rid of the fraction:

**2A/b = h**

**Step #2: **Isolate h

Rearrange the terms to solve for h:

**h = 2A/b**

Question 2: Rearrange t = w/2 to make w the subject.

Answer :**Solution:**

**Step #1:** Isolate w

**t = w/2**

**Step #2:** Multiply both sides by 2 to solve for w:

**2t = w**

Therefore, the equation rearranged to make w the subject is

**w = 2t.**

The knowledge of the ways to transform a formula to another type assists people in dealing successfully with difficult mathematical problems.

Through this particular ability, the interconnection of all the stated variables is uncovered and thus the necessary insights become available.

No matter is the subject of physics or finance, altering the subject is a universal technique that has almost endless applications.

Building this skill is necessary therefore by challenging the reader with different problems enhancing comprehension.

**Question 1:** Make w the subject of the formula** s = w/a**

**Question 2:** Given that x + y = 1 What does y equal?

**Question 3:** Make d the subject of **e = d + 5**

**Question 4:** Rearrange this formula to make c the subject **a = c – w**